Narrow Optical Transitions in Erbium-Implanted Silicon Waveguides

The realization of a scalable architecture for quantum information processing is a major challenge for quantum science. A promising approach is based on emitters in nanostructures that are coupled by light. Here, we show that erbium dopants can be reproducibly integrated at well-defined lattice sites by implantation into pure silicon. We thus achieve a narrow inhomogeneous broadening, less than 1 GHz, strong optical transitions, and an outstanding optical coherence even at temperatures of 8 K, with an upper bound to the homogeneous linewidth of around 10 kHz. Our study thus introduces a promising materials platform for the implementation of on-chip quantum memories, microwave-to-optical conversion, and distributed quantum information processing.

Popular Summary

A breakthrough in quantum information processing is expected once carriers of quantum information, called qubits, can be reliably integrated into silicon—the basis of our current information technology. A common approach to this end is called doping, which means replacing one or several atoms in a crystal with a different atomic species. Previously studied dopants allowed only for coupling between close-by qubits. We demonstrate that this limitation can be overcome by using erbium atoms as dopants, as they coherently couple to optical fields that can be transmitted between remote qubits.

To reliably integrate erbium into silicon, we start from high-purity material, optimize the doping procedure, and use nanophotonic structures that allow for efficient laser excitation using off-the-shelf photonics components. The dopants then emit light with exceptionally small frequency fluctuations, which is a key enabler for the interfacing of remote qubits. As the emission is at a minimal-loss telecommunications wavelength, light can be transmitted efficiently not only between qubits on the same chip but also over large distances using the existing glass-fiber infrastructure.

Our system may open the door for extended quantum networks and distributed quantum computers that are based solely on standard semiconductor and photonics technologies.

Figure 1

Different waveguide geometries used in this work. (a) To confine a single guided mode (colors: intensity profile), rib waveguides are fabricated by partially etching a chip with a $2\mu \mathrm{m}$ FZ ($>10\mathrm{k}\mathrm{\Omega }\mathrm{cm}$) device layer (DL) on top of a $1\mu \mathrm{m}$ buried oxide (BOX). Erbium is implanted at three different energies to give an approximately homogeneous concentration in the waveguide (red profile on the right). (b) Ridge waveguides are fabricated by fully etching a $0.2\mu \mathrm{m}$ thin DL on a $>2\mu \mathrm{m}$ BOX. The intensity profile (colors) shows the fundamental TE mode. The DL consists of CZ material ($>1\mathrm{\Omega }\mathrm{cm}$) or a $0.12\mu \mathrm{m}$ pure CVD layer grown on top of a $0.07\mu \mathrm{m}$ thin CZ seed. To achieve an approximately homogeneous concentration (right), three (CZ, black) or two (CVD, red) different implantation energies are used. (c) In the rib waveguides, the photonic local density of states (LDOS) and the associated Purcell factor in the silicon layer (colors) are independent of the dopant position in the waveguide, leading to an effective Purcell factor $F_P$ of 1 for all emitters. (d) In the ridge waveguides, the radiative decay rate of dipolar emitters oriented along the waveguide width (double arrow) is suppressed ($F_P<1$) or enhanced, depending on its position.

Figure 2

Spectroscopy of erbium-implanted silicon waveguides. (a) Inset: experimental setup. A laser is switched by acousto-optic (AOM) and phase-modulated by electro-optic modulators (EOM). A 99∶1 beam splitter is used to guide the light emitted from the sample in the cryostat to single-photon detectors (SNSPD). Main graph: scanning the excitation laser frequency results in several narrow fluorescence peaks, here shown for the FZ sample. (b) Insertion of a narrow-band optical filter, tuned on resonance with one of the three most prominent peaks (color coding), eliminating the broadband background observed otherwise (which is strongest in the shown CVD samples). Scanning the excitation laser then reveals the excited-state crystal fields of the individual sites. (c) Keeping the laser on resonance with one of the main peaks while scanning the filter, which gives the ground-state crystal fields. The filled triangles in (c) and (b) mark the filter and excitation laser positions, respectively, in (b) and (c).

Figure 3

Inhomogeneous linewidth and optical lifetime. (a) Resonant fluorescence after excitation laser pulses of different frequency. The observed lines are well fit by Lorentzian curves. The observed linewidths in the FZ samples (faint colors) are larger than in the CZ (bright colors) and CVD samples (see Appendix pp5-s2) because of implantation-induced damage. (b) To determine the lifetime, we excite a higher CF level and observe the filtered lowest CF transition. The observed lifetime depends on the site (color) and the waveguide geometry (faint, ridge waveguide; bright, rib waveguide). The slowest decay is observed for site P (green), whereas site A (blue) and B (red) show faster decays. In the ridge waveguides, the spatial variation of the local density of states leads to a slower biexponential (dashed line) rather than a single-exponential (solid line) decay (see Appendix pp7).

Figure 4

Homogeneous linewidth measurement. Top left inset: measurement scheme. The laser is modulated to generate a comb of up to 27 lines with equal separation and amplitude, exciting many subensembles (brown) within the inhomogeneous line of the dopants (dashed line). When the modulation frequency is smaller than the linewidth of the subensembles, saturation leads to a signal decrease (right inset), which is well fit by Lorentzian curves (red solid line) with FWHM down to 18(6) kHz for site A (blue) and 20(4) kHz for site B (red). An upper bound for the homogeneous linewidth is given by half the width of the transient hole (main graph, CVD sample, red and blue data). The data exhibit a $\sqrt{I}$ scaling (lines) down to the lowest intensity that provides sufficient signal to noise (red circle, shown as inset). This indicates that the measured linewidth is determined by power broadening and thus constitutes an upper bound to the homogeneous linewidth of erbium dopants in the investigated nanophotonic silicon waveguides.

Figure 5

Temperature dependence. The temperature of the CVD sample is changed with a resistive heater. The lifetime $\tau$ of the optically excited state, and thus the lifetime limit $1/(2\pi \tau )$ (purple data and line) of the homogeneous linewidth, is independent of temperature, as expected for erbium dopants in the absence of nonradiative decay of the optically excited state. In contrast, the homogeneous linewidth shows an increase with temperature. For site A (blue, main panel) and several input powers (different symbols), the rise is well explained by Orbach relaxation of the spin levels (blue fit curves). From the Orbach coefficient, in the absence of power broadening (black), we expect that the lifetime-limited linewidth may be observed below about 8 K. While site B shows similar temperature dependence (red, inset), the other bright site (green, inset) exhibits much broader lines even at 2 K, owing to its smaller CF level separation.

Figure 6

Preparation of the CVD samples. A commercial SOI wafer with a device layer thickness of $0.07\mu \mathrm{m}$ is exposed to a hydrogen bake. Subsequently, pure silicon is grown by chemical vapor deposition to a total DL thickness of $0.19\mu \mathrm{m}$. In a third step, erbium is implanted with two energies that give an approximately homogeneous dopant concentration in the device layer. Finally, established techniques (electron-beam lithography and reactive ion etching) are used to fabricate nanophotonic waveguides with a width of $0.7\mu \mathrm{m}$. The other samples are prepared in the same way, except that different starting material is used and the CVD step is omitted.

Figure 7

(a) Experimental setup. AOMs are used to generate pulses of controlled duration, amplitude, and frequency shift from a continuous-wave laser. EOM, driven by an arbitrary-waveform-generator (AWG), are used to generate optical sidebands. A fiber-based nonpolarizing beam splitter with a $99:1$ (in some measurements $95:5$) split ratio is used to irradiate the excitation light and guide the fluorescence signal to a SNSPD. The sample is kept in a closed-cycle cryostat on an $XYZ$ nanopositioning stage. (b) Waveguide propagation loss on the CVD samples. The reflected signal is measured for waveguides of different lengths. An exponential fit then allows for extracting the propagation loss for doped (blue) and undoped (red) CVD samples.

Figure 8

Energy of the crystal-field levels of sites A (blue) and B (red). (a) Frequency difference of the CF levels with respect to the ground state of the respective manifold. (b) Level scheme with the corresponding wavenumbers. The excited state includes all CF levels of the ${}^4{I}_{13/2}$ state manifold, whereas in the ${}^4{I}_{15/2}$ ground-state manifold, two levels have not been detected because the filter used only tunes to 1600 nm.

Figure 9

Comparison of the resonant excitation spectrum in the different sample types. Compared to the CVD and CZ samples, the FZ chips exhibit a smaller number of resonant peaks, which is attributed to the higher purity of the starting material. The triangles at the bottom of the third panels indicate different sites that were observed in our earlier work [11], which used different implantation conditions.

Figure 10

Inhomogeneous linewidth comparison. The narrowest lines are obtained in the CZ samples. The FZ samples show an increased linewidth that is attributed to an increased crystal damage caused by the higher implantation energy. The CVD samples show a double-peak structure, which we attribute to the two implanted isotopes.

Figure 11

Homogeneous linewidth comparison. In all samples, the homogeneous linewidth is limited by power broadening, even at the lowest powers that give a sufficient signal.

Figure 12

Excited-state CF levels of site P. Site P is attributed to erbium precipitates as it shows 14 CF levels in the $I_{13/2}$ manifold—twice the number expected for a single erbium site in the absence of a magnetic field. As the smaller CF splitting of this site cannot be resolved well in Fig. 2, this figure shows the data over a smaller wavelength spread. While we can resolve the $I_{13/2}$ levels well by scanning the narrow-linewidth laser, not all $I_{15/2}$ levels are resolved because of the finite 0.11 nm bandwidth of the available wavelength filter.

Figure 13

Fluorescence upon off-resonant excitation in the CVD sample. The samples are excited at two different wavelengths (triangles): 1531.0 nm (orange, with added offset) and 1533.5 nm (blue), which do not coincide with one of the resonances in Fig. 2. The filtered fluorescence signal recorded after the laser pulses shows a peak at the excitation frequency and, in addition, some off-resonant fluorescence at several discrete wavelengths, which we attribute to charge relaxation via an optically active site [21].

Figure 14

Modification of the electric-dipole emission in the different samples. Finite-difference-time-domain calculations are used to simulate the photonic density of states depending on the position in the waveguide (cross-sectional images) and the orientation of the electric dipole (black symbols). From this, the emission rate of erbium dopants is determined. In addition, the probability $\beta$ to emit into the guided mode is calculated. The dimensions of the waveguides differ between samples, as shown in Fig. 1. (a,b) Ridge waveguides used on the CVD and CZ samples. The decay rate can be increased (Purcell enhancement $F_P>1$) or reduced ($F_P<1$) depending on the position. Here, $\beta$ approaches unity for erbium dopants at the waveguide center with a horizontal dipole orientation (top), but it is much smaller for the other dipole orientations. (c) Expected temporal decay of the fluorescence in the ridge waveguides. A Monte Carlo simulation is performed, in which dopants are randomly positioned in the waveguide according to the implantation profile. Then, their dipole decay is averaged, weighted by the $\beta$ factor. The resulting data for different dipole orientations (black line) deviate from a single exponential fit (dashed line). A biexponential decay (solid line) gives better agreement. (d,e) Rib waveguides used on the FZ samples. The Purcell factor is $F_P=1$, almost independent of the position in the waveguide. Thus, one expects a decay with a time constant that is independent of the emitter orientation and that matches the lifetime of the dopants in bulk crystals. The average $\beta$ factor is much lower than in the ridge waveguide geometry, and mostly light of transversal polarization (top and center panels) is emitted into the guided mode.

Figure 15

Comparison of two different techniques to measure the homogeneous linewidth. At the same pulse parameters, the technique introduced in Ref. [11] [blue data and Lorentzian fit with FWHM 3.8(1) MHz] and used in Sec. 6 gives a significantly better signal-to-noise ratio than the pump-probe scheme introduced in Ref. [24] [orange data and fit with FWHM 3.8(4) MHz]. The $y$ axis shows the detected photons per repetition, divided by the detection time window.

Figure 16

Measurement of the homogeneous linewidth using one EOM (a) or three concatenated EOMs (b) to generate 3 or 27 lines. The different randomly chosen colors indicate measurements at different power. At the same power-broadened homogeneous linewidth, a better signal-to-noise ratio is obtained when using three EOMs instead of only one.

Figure 17

Effect of persistent spectral hole burning on the homogeneous linewidth. The homogeneous linewidth is measured using the scheme described above. In the first curve (blue), the laser frequency is changed randomly after each iteration of the transient-hole-burning sequence. If the laser frequency is not shifted (orange), broader lines are obtained at low laser powers, which is attributed to persistent spectral hole burning.

Figure 18

Comparison of the key parameters of erbium dopants in various hosts. Sites A and B studied in this work exhibit the largest CF splittings and the fastest radiative decay, offering unique promise for quantum applications.